Calibration of an analogue probe

ABSTRACT

A method of calibrating a probe mounted on a machine in which the probe has a probe calibration matrix which relates the probe outputs in three orthogonal axes to the machine&#39;s X, Y and Z coordinate system. A datum ball mounted on the machine is bi-directionally scanned by the probe in one or more planes. For each plane, the mean direction of two approximate probe vectors in the plane is rotated about an axis orthogonal to that plane until the apparent material condition from the scan in each direction is the same. This process may be iterative. The mean values of the directions of the probe vectors for each plane are rotated, thus forming a corrected probe calibration matrix. The datum ball is preferably bi-directionally scanned in three orthogonal planes.

[0001] The present invention relates to a method of calibration foranalogue probes. The method has particular reference to the calibrationof analogue probes which have a stylus for contacting a workpiece, andwhich is mounted on a mechanical suspension, for example a springsuspension.

[0002] Analogue probes of this type are well known and an example ofsuch a probe is described in our UK Patent No. 1,551,218. This patentdescribes a probe suspension mechanism which comprises threeorthogonally arranged pairs of parallel springs connected in seriesbetween a fixed point on the probe housing and a movable member to whicha workpiece contacting stylus is connected.

[0003] During a measuring operation on a workpiece using such a probe, amachine on which the probe is mounted is driven towards the workpiece tobring the stylus into contact with the workpiece surface at variouspoints on the surface. When the stylus contacts the workpiece the styluswill be deflected as the machine continues to move, and measuringtransducers within the probe generate outputs representing deflectionsof the probe stylus along three orthogonal axes. These axes are referredto as the a, b and c axes of the probe.

[0004] Ideally it would be arranged that the a, b, and c axes of theprobe are aligned with the X, Y and Z coordinate axes of the machinewhen the probe is mounted on the machine, so that the measureddeflections of the probe stylus will take place along the X, Y and Zaxes of the machine. However, such alignment is not always possible toachieve.

[0005] Also, if there is any mis-alignment between the three probe a, band c axes, such that they are not orthogonal, then deflection of thestylus, for example, nominally in the a direction can give rise todeflections in the b and c directions also.

[0006] Additionally, the scaling factors of the three probe axes will,in general, deviate from their nominal values.

[0007] Therefore, it is usual to calibrate the probe and machine systemto determine the effects of any such mis-alignments and scaling errors,and thereafter to correct any measurements made on a workpiece for theseeffects.

[0008] One method of performing the calibration which is described inour International Patent Application No. WO00/25087 is to mount acalibration artefact (usually a reference sphere of known diameter) onthe machine, and to drive the probe towards the artefact, for example,along one of the machine axes, until an increase in the output of themeasuring devices of the probe above a pre-determined threshold levelindicates that contact with the surface of the artefact has been made.After stylus contact has been confirmed, a set of machine X, Y, Z andprobe a, b, c coordinate data are taken. Machine movement continuesuntil the machine has moved a selected distance beyond the confirmedcontact point, and a further set of X, Y, Z, and a, b, c coordinate dataare taken.

[0009] The changes in the a, b, c outputs of the probe's measuringtransducers in the three axes are recorded and correlated with thechanges in the readings of the machine's measurement devices along eachof the three machine axes. This procedure is repeated for two otherorthogonal directions, which may be the other two machine axes, and fromthe sets of readings a probe transformation matrix can be establishedwhich relates the probe outputs in the a, b and c axes to the machine'sX, Y and Z coordinate system. This involves solving the ninesimultaneous equations relating the a, b, and c axis data to each of theX, Y, and Z axes. This process may be repeated for one or more furtherdeflections but normally only relatively few data points are taken.

[0010] Once the transformation matrix has been established the relevantmachine axis components of the probe deflections can be obtained bymultiplying the relevant probe output by the relevant matrix term.

[0011] The key assumption in this calibration is that the machinemovement mirrors the movement of the stylus tip relative to the probe.However, this assumption becomes invalid when the stylus slips on thesurface of the sphere.

[0012] There are two factors which can cause the stylus to slip on thesphere surface;

[0013] i) the machine may not go down the commanded direction accuratelyenough to prevent slippage,

[0014] ii) the probe force and deflection vectors may not coincideclosely enough to prevent slippage.

[0015] Although the sensitivities of the probe axes are accuratelydetermined by this method, side slip of the stylus generates falsedirections for the probe axes.

[0016] Furthermore, when scanning with the calibrated probe, tipfriction drag causes a significant component of probe displacement inthe negative scan direction.

[0017] The combination of the false directions of the probe axesmentioned above with tip friction drag causes an error in the apparentmaterial condition of the surface (i.e. in the direction normal to thesurface).

[0018] The present invention provides a method of calibrating a probe,said probe being mounted on a machine and having a stylus with aworkpiece contacting tip and having a probe calibration matrix whichrelates the probe outputs in three orthogonal axes to the machine's X, Yand Z coordinate system, comprising the steps of:

[0019] bi-directionally scanning a datum ball in at least one plane andfor each plane, rotating the mean direction of two approximate probevectors in the plane about an axis orthogonal to the that plane untilthe apparent material condition from the scan in each direction is thesame;

[0020] taking the rotated mean values of the directions of the probevectors for each plane and thus forming a corrected probe calibrationmatrix.

[0021] Individual probe vectors in each plane may be allowed to vary inmagnitude and direction providing the mean vector direction remainsunchanged.

[0022] The methods of the invention will now be more particularlydescribed with reference to the accompanying drawings in which:

[0023]FIG. 1 illustrates a scanning probe with its stylus in contactwith a reference artefact,

[0024]FIG. 2 shows a plot of probe deflections versus machine movementin one of the X Y Z axes of the machine,

[0025]FIG. 3 shows a scanning probe with its stylus lagging due tofriction; and

[0026] FIGS. 4A-C show the bi-directional scanning of a datum ball inthree orthogonal planes.

[0027] Referring now to FIGS. 1 and 2, there is shown an analogue probe1 mounted on a machine quill (not shown) and which has a stylus 2 with astylus ball 3 at its free end. The stylus is shown in contact with areference sphere of known radius R and having its centre O at positionX1, Y1, Z1 in the machine axis coordinates. The stylus ball has a radiusr which is to be determined, along with the position of the centre ofthe sphere and the probe transformation matrix.

[0028] As a first step in the calibration method the probe must be“zeroed” in its free condition. This simply involves taking readingsfrom the probe measurement transducers when no contact force is actingon the stylus and setting these to zero in all three axes, oralternatively storing these readings so that they can be subtracted fromall subsequent readings.

[0029] The next step is to make an estimate of the position of thecentre of the sphere, by taking measurements of points at four positionsaround the surface of the sphere from which the position of the centrecan be calculated in known manner, and using a relevant default probetransformation matrix as a starting point. This step is needed becausethe calibration method requires the sphere to be contacted at least at 9points, but up to as many as may be required with a reasonabledistribution over its surface, taking account of obstructions, and it isimportant that the machine should be driven so the probe will contactthe surface at approximately the right positions on the surface of thesphere. However, it is not important that the position of the centre ofthe sphere is known accurately at this stage.

[0030] The calibration method requires that for each of the plurality ofpoints of the calibration algorithm, the probe stylus is driven by themachine into contact with the sphere in a direction which is nominallynormal to the sphere surface. After the stylus ball has contacted thesurface of the sphere, the machine continues to drive the probe in thesame direction until the deflection of the stylus exceeds the requiredcalibration deflection. The magnitude of this deflection is determinedby the deflections which will occur in practice when the probe is beingused to measure a workpiece.

[0031] Once the required deflection of the stylus has been achieved themachine is stopped and reversed along its approach path, and readingsare taken simultaneously at regular intervals, of the outputs of themeasuring devices of the machine and of the measuring transducers in theprobe, to provide the a, b and c outputs of the probe synchronised withthe X, Y and Z coordinates of the machine position. This processcontinues until the probe stylus leaves the surface and for a smalldistance thereafter to take account of noise and time lags in the probeoutputs.

[0032] This data may now be used to calculate the X, Y, and Z axispositions of the machine at zero probe deflection for each of the pointson the sphere, for example, by fitting the data for each point to anequation of the form;

x=k1.a+k2.b+k3.c+k4

[0033] and then extrapolating to zero, i.e. x=k4.

[0034] Because the reference sphere and the stylus ball are bothspecified as being accurately spherical, it follows that all of theseextrapolated points must be on the surface of a sphere of radius R+r.From the points which have been calculated, the radius R+r and theposition of the centre of the sphere can now be calculated moreaccurately using a standard multi-point sphere fit function, for examplethe least squares best fit method. Since the radius R of the sphere isknown the radius r of the stylus ball can now be determined.

[0035] The above-described calibration process is described inWO00/25087. This process provides a probe matrix optimised for oneradial deflection of the stylus, and, if desired, further calculationscan be carried out for other deflections of the probe within the normalmeasuring range.

[0036] The benefit of this calibration process is that the solerequirement is that the stylus ball remains on the surface of thereference sphere while the data is being gathered at each of the points.It is also important that the acquisition of the measurement data fromthe measuring devices of the machine giving the X, Y and Z coordinatesat each point is adequately synchronised with the data coming from theprobe measuring devices which provide the probe axis a, b and c data.

[0037] The matrix generated above is only approximate since frictioneffects may distort direction and magnitude of the probe axes.

[0038] When scanning with the calibrated probe frictional drag on theprobe tip 3 causes a significant component of probe displacementparallel to the surface 4 in the negative scan direction as seen in FIG.3.

[0039] The combination of the false directions of the probe axes causedby slippage (the coefficient of friction of stylus tips is very low)with tip friction drag causes an error in the apparent materialcondition of the surface.

[0040] This error is readily seen when scanning in opposite directionsalong a surface. Apparent changes in the material conditions of thesurface are detected in the two opposite directions caused by the probelag due to friction. The invention lies in using these differences tofine tune the vector directions. This is done by rotating the probematrix to make the apparent friction angles appear nominally the same ineach direction. This may be iterative.

[0041] In a perfect system without slip, the probe tip should have adisplacement which exactly mirrors that of the CMM when the CMM is moveda given distance and direction against a surface. In this perfect systemthe probe matrix could, for example be: $\begin{matrix}100 \\010 \\001\end{matrix}$

[0042] This is using the convention below which will be usedsubsequently.

[0043] a (X term) b(X term) c(X term)

[0044] a (Y term) b(Y term) c(Y term)

[0045] a (Z term) b(Z term) c(Z term)

[0046] However, false directions may be acquired for some probe axesduring calibration, for example if slippage occurred. Assuming, forillustration, that the slippage was such as to cause the probe a+ vectorto appear to be +1° from its true direction in the XZ plane only. Afalse probe matrix would then be generated, as shown below.$\begin{matrix}{\cos \quad 1^{0}} & {0\quad 0} \\0 & {1\quad 0} \\{\sin \quad 1^{0}} & {0\quad 1}\end{matrix}$

[0047] In this case the significant error is sin1° (i.e. the a(Z term)).Thus when measuring in the Z direction, any probe deflection in theprobe “a” direction will cause a measuring error of asin1°.

[0048] When scanning a surface in ±a directions, friction drag causesthe ±a probe deflections in the opposite direction. Thus in this casethe ±asin1° error in Z when scanning over a plane is caused by the probedragging with a friction angle of 1°.

[0049] To determine the true probe axis directions the datum ball isscanned bi-directionally in each of three nominally orthogonal planesand synchronous machine and probe readings are obtained. These planesmay be the XY plane, YZ plane and XZ plane.

[0050] For each scan the apparent friction angle is determinedcontinuously from the differences between the measured surface normaland the probe deflection direction. Apparent friction angle versusangular position around the ball may be plotted for each scan direction.The errors in probe axis directions cause the mean lines to beasymmetric either side of zero friction angle.

[0051] Firstly the datum ball is scanned in the XY plane in both theclockwise and anti-clockwise directions as shown in FIG. 4A. The meandirection of the two approximate probe vectors in the XY plane (i.e. aand b) is rotated about the Z axis iteratively until the apparentfriction angle for either direction of scan is equal.

[0052] The datum ball is then scanned in the YZ plane as shown in FIG.4B. Again the datum ball is scanned in both clockwise and anti-clockwisedirections. This time the mean direction of the two approximate probevectors in YZ plane (i.e. b and c) is rotated about the X axisiteratively until the apparent friction angle for either direction isequal.

[0053] Finally the datum ball is scanned in the XZ plane in bothclockwise and anti-clockwise directions as shown in FIG. 4C. In thiscase the mean direction of the two approximate probe vectors in the XZplane (i.e. a and c) is rotated about the Y axis iteratively until theapparent friction angle for either direction of scan is equal.

[0054] It can be seen that after the three scans described above thereare three resulting mean vectors, a/b, b/c and c/a. Without changing anyof these mean directions (e.g. by rotating a and b equally andoppositely in the ab plane) individual probe axis vector directions andmagnitudes-are varied to minimise the sum of the radial errors squared.This is a standard calibration technique and will not be discussedfurther.

[0055] This method has the advantage that once the six scans of thedatum ball have been completed (i.e. two in each plane), the existingdata is used to optimise the probe matrix iteratively without anyfurther data being required.

[0056] A further benefit is that the number of touch points required forcalibration with this method is reduced. Good results may be achieved bycombining a 9 point touch initial matrix with the six scan refinementabove. However in practice 13 points are preferred as this gives betterestimates of the position of the reference ball and the diameter of theprobe tip, both of which are required for subsequent measuring tasks.

[0057] This method of enhanced probe calibration is also suitable foruse in touch trigger measurement.

[0058] The invention is not limited to bi-directionally scanning thedatum ball in three orthogonal planes. The method may be carried out ina subset of this, for example just one plane or in two-orthogonalplanes.

[0059] Furthermore, the method may be carried out by bi-directionallyscanning the datum ball in planes which are not orthogonal to oneanother.

1. A method of calibrating a probe, said probe being mounted on amachine and having a stylus with a workpiece contacting tip and having aprobe calibration matrix which relates the probe outputs in threeorthogonal axes to the machine's X, Y and Z coordinate system,comprising the steps of: bi-directionally scanning a datum ball in atleast one plane and for each plane, rotating the mean direction of twoapproximate probe vectors in the plane about an axis orthogonal to thethat plane until the apparent material condition from the scan in eachdirection is the same; taking the rotated mean values of the directionsof the probe vectors for each plane and thus forming a corrected probecalibration matrix.
 2. A method of calibrating a probe according toclaim 1 wherein the individual probe vectors in each plane are allowedto vary in magnitude.
 3. A method of calibrating a probe according toany preceding claim wherein the individual probe vectors in each planeare allowed to vary in direction.
 4. A method of calibrating a probeaccording to any preceding claim wherein the one or more planes aresubstantially orthogonal to each other.
 5. A method of calibrating aprobe according to any preceding claim wherein the one or more planescomprise three planes substantially orthogonal to each other.
 6. Amethod of calibrating a probe according to any preceding claim whereinthe process of rotating the mean direction of the two approximate probevectors in the plane about an axis orthogonal to that plane isiterative.
 7. A method of calibrating a probe according to any precedingclaim wherein the probe is an analogue probe.
 8. A method of calibratingan analogue probe, said analogue probe mounted on a machine and having astylus with a workpiece contacting tip and having a probe calibrationmatrix which relates the probe outputs in three orthogonal axes to themachine's X, Y and Z coordinate system, comprising the step of: (a)bi-directionally scanning a datum ball in a first plane and rotating themean direction of two approximate probe vectors in said first planeabout an axis orthogonal to the first plane until the apparent materialcondition from the scan in each direction is the same; (b)bi-directionally scanning said datum ball in a second plane orthogonalto the first plane and rotating the mean direction of two approximateprobe vectors in said second plane about an axis orthogonal to thesecond plane until the apparent material condition from the scan in eachdirection is the same; (c) bi-directionally scanning said datum ball ina third plane orthogonal to the first and second planes and rotating themean direction of two approximate probe vectors in said third planeabout an axis orthogonal to the third plane until the apparent materialcondition from the scan in each direction is the same; (d) taking therotated mean values of the directions of the probe vectors of steps (a),(b) and (c) and thus forming a corrected probe calibration matrix.